If it were me I would just go ahead and go right to El Capitan. I've ran it on even older (09 27" iMac and 09 17" MacBook Pro) machines than the 2011 MBA you mention. They have ran great and can only imagine a 2011 would run even better. Plus it would take out the need for a lot of maintenance you would have to do on visits due to SIP (System Integrity Protection) all sorts of things are kept protected like permissions and such. Plus not to mention all the latest security updates, which is pretty important for any computer.

Your only legal choices are Mountain Lion ($19.99 at Apple) or El Capitan (free from the App Store). Mavericks and Yosemite were removed from the Apple App Store as new OS were released. So as T'hain Esh Kelch said, you can only download Mavericks and Yosemite if previously purchased from the App Store by going the the Purchased tab.

thanks all! i had noticed the $20 mountain lion from apple, so it was either that or el cap. good to know. yeah, i'll go ahead and put el cap on her computer. it can't be that bad - given the incramental differences between mba iterations. i use a 2013 mba with el cap, and i have no qualms. cheers

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